Hello good MHF folk. I'm getting very frustrated with a few exercises in Stroud's Advanced Engineering Mathematics 5th ed. I just can't get to the answers provided, I'm hoping someone may be able to help me

First one is this. Sketch the graph then find the laplace transform of:

$\displaystyle f(t)\left\{\begin{matrix}3^{-2t} & 0\leq t < 2\\ 0 & 3 \leq t \end{matrix}\right.$

I can draw the graph ok, I understand that. And my answer is almost the same but there is an

$\displaystyle e^{-6}$

in the given answer that I just don't understand... Here is their answer:

$\displaystyle F(S) = \frac{1}{s+2} (1 - e^{-6}e^{-3s})$